Differential Evolution for Finite Element Model Updating: Algorithm and Application in Structural Analysis

Abu Abed, Wassim · 2024 · Crossref

DOI: 10.58286/29656

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the challenge of Finite Element Model (FEM) updating in Structural Health Monitoring, where accurate numerical models are essential for diagnostic and prognostic purposes. The core problem is calibrating model parameters to minimize the discrepancy between numerically calculated structural responses and measured data. The authors propose an updating algorithm based on Differential Evolution, a population-based global optimization method, enhanced by the use of continuous interpolation functions to reduce the dimensionality of the search space. This approach aims to accelerate convergence and improve solution reliability without compromising accuracy. The methodology employs Differential Evolution to optimize the error function, defined as the difference between measured and calculated responses. To address the high computational cost associated with population-based methods, the authors integrate Shepard interpolating functions. These functions allow parameter values to be adapted at a few supporting points and interpolated across the finite elements, significantly reducing the search space dimension ($d$). The algorithm was verified using three hypothetical study cases with artificially generated data derived from FEM simulations. The cases included: (1) a static analysis of a 10 m single-span concrete beam with a damaged region, updated using displacement data; (2) a static analysis of a 2D single-span concrete road bridge, also updated using displacement data; and (3) a dynamic analysis of a 32 m train bridge subjected to an ICE 1 train load, updated using acceleration data. The results demonstrate that reducing the search space dimension via Shepard interpolation effectively speeds up convergence and enhances the reliability of finding accurate solutions. In the beam example, a search space dimension of $d=3$ yielded an exact reproduction of the modulus of elasticity distribution with lower computational complexity ($NUM_{fem} \approx 15 \cdot 111$) compared to $d=10$, which produced non-unique results and higher complexity ($NUM_{fem} \approx 50 \cdot 200$). Increasing the amount of measured data, such as using a moving load instead of a static point load, further improved accuracy. The road bridge case achieved a mean absolute error of $E \le 10^{-9}$ with $d=7$, while the dynamic train bridge case achieved $E \le 10^{-4}$ with $d=3$, both accurately reproducing the expected modulus of elasticity distributions. The study concludes that combining Differential Evolution with Shepard interpolation is an efficient strategy for FEM updating, balancing computational cost with solution accuracy. The authors note that the placement of Shepard supporting points significantly influences accuracy and indicate that future work will focus on optimizing these positions. Additionally, further developments will explore other variations of Differential Evolution and the optimization of algorithm hyperparameters using phase portrait concepts to further boost performance and convergence reliability.

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• perception reaction time